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Thermodynamic reassessment of Gd–Ni system
Accepted Manuscript Thermodynamic reassessment of Gd–Ni system Z. Rahou, K. Mahdouk PII:
S0925-8388(15)30320-0
DOI:
10.1016/j.jallcom.2015.06.201
Reference:
JALCOM 34608
To appear in:
Journal of Alloys and Compounds
Received Date: 18 May 2015 Revised Date:
23 June 2015
Accepted Date: 24 June 2015
Please cite this article as: Z. Rahou, K. Mahdouk, Thermodynamic reassessment of Gd–Ni system, Journal of Alloys and Compounds (2015), doi: 10.1016/j.jallcom.2015.06.201. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Thermodynamic reassessment of Gd–Ni system Z. Rahou∗ and K. Mahdouk Laboratory of Thermodynamics and Energetics (L.T.E), Faculty of Sciences, Ibn Zohr University, B.P. 8106, Agadir, Morocco. ∗ Corresponding author; phone: +212-661625347; email: [email protected].
Abstract
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By means of CALPHAD (CALculation of PHAse Diagrams) approach, the phase diagram and thermodynamic data of the Gd–Ni system were critically assessed. The Gd–Ni system contains four solution phases (liquid, face-centered cubic FCC_A1, body-centered cubic BCC_A2 and hexagonal close-packed HCP_A3) modeled with the Redlich-Kister polynomials and seven intermetallic compounds Gd3Ni, GdNi, GdNi2, GdNi3, Gd2Ni7, GdNi5 and Gd2Ni17, which are all treated as stoichiometric compounds. A set of self-consistent thermodynamic parameters describing various phases in this binary system was obtained. The phase diagram and thermodynamic quantities calculated from assessed parameters agree well with experimental data.
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Keywords: Gd–Ni system, thermodynamic assessment, phase diagram, Calphad approach.
1. Introduction
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The intermetallic compounds formed by rare earth (RE) elements and transition metals (TM) are of particular interest regarding to their potential usage as high value functional materials, such as permanent magnets [1,2] and hydrogen storage materials (reversible absorption of a large quantity of hydrogen gas at room temperature and nearly at atmospheric pressure) [3,4]. Moreover, many ternary Al–TM–RE systems form amorphous alloys with interesting mechanical properties [5] and some rare-earth/transition metal oxides are candidate materials for solid oxide fuel cells [6]. Furthermore, the rare-earth/3d transition metal intermetallic compounds were suggested as being promising candidates for room temperature magnetic refrigeration based on magneto-caloric effect (MCE) [7,8] who has attracted more attention for improved energy efficiency and environmental friendliness compared with traditional compression/expansion gas refrigeration [9,10].
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On the other hand, the knowledge of thermodynamic data and phase diagrams is essential for developing and checking models of phase transformations, coupling thermodynamics with kinetics [11]. The purpose of the present work is (1) to evaluate recent experimental phase diagram and his relative thermodynamic data and (2) to provide a set of self-consistent parameters for calculation of the phase equilibria and thermodynamic properties in the Gd–Ni binary system using the CALPHAD method [12] and the Thermo-Calc software package [13].
2. Thermodynamic models 2.1. Pure elements The stable forms of the pure elements at 298.15K and 1 bar were chosen as the reference states of the system. For the thermodynamic functions of the pure elements in their stable and metastable states, the phase stability for the element i in ϕ status is given as: 0 φ ( T ) = G φ ( T ) − H SER = a + bT + cT ln T + dT 2 + eT 3 + fT − 1 + gT 7 + hT − 9 Gi i i
1
(1)
ACCEPTED MANUSCRIPT where H iSER (298.15 K ) is the molar enthalpy of the so-called “Standard Element Reference” (SER), i.e., the enthalpies of the pure elements in their defined reference state at 298.15 K and 1 bar; T is the absolute temperature; Giφ (T ) is the absolute molar Gibbs energy of the element i (i = Gd and Ni) with structure ϕ in a non magnetic states. In thermodynamic study, absolute energy is not of importance, so the relative value of Gibbs energy 0Giφ (T ) is adopted in CALPHAD approach. The Gibbs energy of the element i, 0Giφ (T ) , in its
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SER state is denoted by GHSERi , i.e. hcp 0 hcp SER GHSERGd = GGd (T ) = GGd (T ) − H Gd (298.15K ) fcc 0 fcc SER GHSERNi = GNi (T ) = GNi (T ) − H Ni (298.15 K )
(2)
(3)
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In the present work, the Gibb energy for the pure element Ni was taken from the SGTE compilation of Dinsdale [14], while that relative to the pure element Gd was taken from the work of Huasen et al. [15] who has evaluated the properties of the Gd element. We note that Dinsdale [16] has recently updated his SGTE-Pure database to incorporate the work of Huasen et al. [15].
2.2. Solution phases
The substitutional solution model was employed to describe the solution phases including Liquid, FCC_A1, BCC_A2 and HCP_A3. The molar Gibbs energy of the solution phase ϕ (ϕ = Liquid, FCC_A1, HCP_A3 and BCC_A2) can be expressed as: mg φ φ 0 φ 0 φ E φ Gm +
Gm
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G m = x Gd GGd + x Ni G Ni + RT ( x Gd Lnx Gd + x Ni Lnx Ni ) +
(4)
where Gmφ is the molar Gibbs energy of a solution phase ϕ; 0Giφ is the molar Gibbs energy of the element i (i = Gd or Ni) with the structure ϕ in a non-magnetic state; xi the mole fraction of component i, R gas constant, T temperature; EGmφ the excess Gibbs energy, and
mg
G mφ is the magnetic
φ
G m = x Gd x Ni ∑ j
j φ j LGd , Ni ( x Gd − x Ni )
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contribution to the Gibbs energy. The excess Gibbs energy of phase ϕ can be expressed by the Redlich–Kister polynomials [17] as: (5)
j φ here LGd , Ni (j = 0, 1, 2,…) is the interaction parameter between elements Gd and Ni and is
formulated as temperature dependent : j φ
LG d , N i = a j + b j T + c j TLnT + d j T
2
+ e jT
3
+ f jT
−1
+ g jT
7
+ hjT
−9
(6)
where aj, bj, cj, dj, ej, fj, gj and hj are model parameters to be optimized. In most cases, only the two first terms of the above equation are used.
2.3. Intermetallic compounds All the intermetallic compounds α-Gd3Ni, β-Gd3Ni, GdNi, GdNi2, GdNi3, Gd2Ni7, GdNi5 and Gd2Ni17 were treated as stoichiometric phases in the Gd–Ni binary system because no available experimental data reports the existence of an homogeneity range for these compounds. The Gibbs 2
ACCEPTED MANUSCRIPT energy of a GdANiB compound is given as: 0
Gd Ni Gm A B =
A
0
A + B
hcp GGd +
B A + B
0
fc c m g G d A N iB G N i + a + bT + Gm
(7)
hcp where 0 GGd and 0 G Nfci c are the Gibbs energies of the respective pure elements Gd and Ni in the non-
magnetic hcp and fcc structure respectively. The parameters a and b are evaluated in the present work.
GmGd A NiB is the magnetic contribution to the Gibbs energy.
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mg
As can be seen in table 1, the Curie temperatures of the intermetallic compounds in the Gd–Ni system, available in the literature, are much below 298.15 K. For this reason, we have not taken into account the contribution of the magnetic term in our calculations.
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3. Bibliographic description of the Gd–Ni system 3.1 Equilibrium diagram
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The Gd–Ni phase diagram has been investigated in 1961 by Spedding et al. [22], Novy et al. [23] and Copeland and Kato [24]. The three diagrams are in a general agreement, showing two congruent melting compounds and three eutectic reactions. Note that Gd2Ni17 with a stoichiometric ratio of 2:17 reported by Novy et al. [23] was widely accepted although a ratio of 2:15 proposed by Copeland et al. [24].
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Buschow and Van Der Goot [25] examined annealed samples of Gd2Ni7 for 2 to 4 weeks. They found that the main phase was hexagonal when samples were quenched from 1200 °C and rhombohedral when annealed at 700 °C. Consequently, they suggested that the hexagonal structure is the high-temperature form, and the rhombohedral type is the low-temperature form. Both of these structures always coexisted in the studied samples, and the temperature of the allotropic transition was not determined.
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The Gd–Ni phase diagram was experimentally reinvestigated in 1986 by Pan et al. [26] using X-ray diffraction (XRD) and differential thermal analysis (DTA) and assessed in 1991 by Pan and Nash [27]. The following nine phases were supposed to exist: Gd3Ni, Gd3Ni2, GdNi, GdNi2, GdNi3, Gd2Ni7, GdNi4, GdNi5 and Gd2Ni17. Among these compounds, GdNi and GdNi5 melt congruently, while the others are formed by peritectic reactions. Three eutectic reactions occur: L↔ Gd3Ni + Gd3Ni2 (635℃, ～32 at.% Ni), L ↔ GdNi2 + GdNi2 (880℃～56 at.% Ni) and L ↔ Gd2Ni17 + fcc-Ni (1275℃, ～95 at.% Ni). Neither Gd in Ni nor Ni in Gd exhibits any detectable solid solubility [26]. The experimental results obtained by Pan et al. [26] and by Copeland and Kato [24] have been used for a thermodynamic assessment carried out by Xia and Jin [28] using the CALPHAD technique. However, the results obtained by these authors present large discrepancies with the experimental data, and the calculated enthalpies of formation are too less negative and seem to be inconsistent. Using XRD at room temperature, DTA, electromotive force (EMF) measurements, Dischinger and Schaller [29] investigated this phase diagram over the entire range of composition. In comparison with the data of Pan et al. [26] there is an excellent accordance concerning the peritectic and the eutectic temperatures and a good accordance concerning the melting point of the compound GdNi5. However, a discrepancy of about 300 K exists concerning the melting point of the GdNi compound.
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ACCEPTED MANUSCRIPT According to Copeland and Kato [24], the Gd3Ni2 and GdNi4 phases reported by Novy et al. [23] and Pan et al. [26] do not exist. This result was confirmed in a recent study of the ternary Gd–Ni– V system by Zhong et al. [30]. Similarly, no evidence was found to support the existence of Gd3Ni2 and GdNi4 in the experimental study of the ternary Gd–Mn–Ni system by Yinghong et al. [31]. Coplend and Kato [24] showed some solubility of Ni in Gd, Gd in Ni, and Ni in GdNi5, but no detailed information was given. Other investigators did not observe these solubilities. All intermetallic phases were suggested to be a line compound by [23], [26] and [29].
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More recently, the Gd–Ni phase equilibria was critically reinvestigated by Xu et al. [32] using scanning electron microscopy with energy-dispersive X-ray spectrometry (SEM/EDS), XRD and differential scanning calorimeter (DSC) measurements realized on samples over the entire composition range. Except the confirmation of the absence of Gd3Ni2 and GdNi4 compounds, the shape of this recent phase diagram is consistent with the results of Dischinger and Schaller [29]. However, discrepancies with the results of Pan et al. [26] was noted especially regarding the congruent melting temperature of GdNi. In the work by Xu et al. [32], the DSC curve for the Gd-20 at.% Ni sample exhibits a small pic at 911 K attributed by these authors to an allotropic transformation of Gd3Ni.
3.2 Thermodynamic data
3.3 Crystallographic data
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Many researchers investigated the thermodynamic properties of Gd–Ni intermetallic compounds. The enthalpies of mixing of liquid alloys were determined at 1750 K over the entire range of composition by Nikolaenko [33]. Enthalpies of formation for several Gd–Ni intermetallic compounds have been determined by calorimetry by Colinet et al. [34], Schott and Sommer [35] and Deodhar and Ficalora [36]. Using direct synthesis calorimetry, Guo and Kleppa [37,38] measured the standard enthalpies of formation of GdNi and GdNi5 compounds. Nourry et al. [40] measured experimentally the Gibbs energies of formation of some Gd–Ni intermetallic compounds. The predicted enthalpies of formation of Gd–Ni alloys from the semi-empirical model of Miedema et al. [39] are also available in the literature.
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The available crystallographic data of Gd–Ni intermediate phases are compiled in Table 2.
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4. Assessment procedure
The thermodynamic optimization of the model parameters of the Gibbs energy expressions is an application of the CALPHAD technique with the help of the PARROT module of the Thermo-Calc software developed by Jansson [49] and Sundman et al. [13]. Its procedure consists of the choice of thermodynamic models for the Gibbs energy of the individual phases as previously described, the analysis of the all related experimental data available, and the computer-aided nonlinear for minimizing the square sum of the errors between the experimental data and the computed values. In the beginning of the assessment, each set of experimental data was given a certain weight. The weights were changed systematically during the optimization until most of experimental data was accounted for within the claimed uncertainty limits. The optimization was carried out by steps. The thermodynamic parameters for the intermetallic compounds were optimized at the first stage based on the available experimental standard enthalpies of formation for the Gd–Ni intermetallic compounds and the phase boundaries information. Then experimental data related to invariant equilibria have been added to the calculation. All the parameters were finally evaluated together to give the best 4
ACCEPTED MANUSCRIPT description of the system. We note that we have neglected the solubilities in the FCC_ A1, BCC_A2 and HCP_A3 terminal solid solutions in accord with the recent experimental results [32]. This was realized by assigning a large positive value to the j LφNi ,Gd interaction parameter of Eq (5), i.e. 0
L GH dC P, N _i A 3 =
0
L GB Cd C, N _i A 2 =
0
L GF Cd C, N_i A 1 = 1 0 4
(7)
5. Results and discussion
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Thermodynamic parameters for all condensed phases in the Gd–Ni binary system obtained in the present work are summarized in Table 3. In Table 4, we give invariant reactions data for this binary system. Good agreement has been realized between the calculated results and the recent experimental data reported by Xu et al. [32].
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The calculated phase diagram of the Gd–Ni system is illustrated in Fig. 1. In Fig. 2 we compare our calculated phase diagram with the experimental data reported by Xu et al. [32], Pan et al. [26] and Dischinger and Schaller [29]. The phase diagram obtained in this work is in good agreement with that established recently by Xu et al. [32]. The incompatible asymmetry of the liquidus phase [50,51] on the left and right sides of the GdNi5 compound was corrected in the course of this study (Fig.2). Indeed, according to Okamoto and Massalski’s studies [50, 51], judgment about asymmetry of liquidus curves can be made comparing the ratio of the width of the two phase fields on each side of a compound at the same temperature. If the width on one side of the compound is either one half or double that on the other side, the asymmetry may be considered clearly unusual.
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As mentioned previously, the enthalpies of formation of the Gd–Ni intermetallic compounds are measured by several authors. In general, direct calorimetric measurements are considered to be the most reliable, so the values obtained by Guo and Kleppa [37, 38] were used in the present study with high weights. Fig. 3 shows the standard enthalpies of formation of Gd–Ni intermediate phases together with the predicted values by the Miedema model [39] and with the experimental data determined by Colinet et al. [34], Schott and Sommer [35], Deodhar and Ficalora [36] and Guo and Kleppa [37, 38]. A reasonable agreement is noted between the calculated results and the experimental values determined by calorimetry. The enthalpies of formation for many compounds predicted by Miedema model [39] are usually more exothermic compared to the calorimetric data and they may be considered using precaution. The enthalpy of formation determined by Deodhar and Ficalora [36] for GdNi2 using calorimetry [36] is less negative than our calculated one. This value is also less negative compared to the other experimental values obtained by Colinet et al. [34] and Schott and Sommer [35]. The discrepancy between the experimental results is certainly due to the relative purity of the starting materials [52,53] and to the fact that the rare earth elements are largely reactive with crucibles and containers, particularly at high temperatures [54]. We note that the enthalpies of formation of Gd3Ni and GdNi2 calculated by Xia and Jin [28] are too less negatives and differ from the experimental values of Colinet et al. [34] by 13.5 kJ/mol and 23.7 kJ/mol respectively. Fig. 4 presents the calculated enthalpy of mixing of liquid at 1750K in the Gd–Ni system with the experimental data determined by Nicolaenko [33]. The calculated values are satisfactorily consistent with the measured data in Ref. [33]. Gibbs energies of formation of intermetallic compounds at 1113K were further calculated and compared with data measured by Nourry et al. [40] in Fig. 5. Good agreement was realized between the calculated values and experimental results for GdNi5 and GdNi3 intermetallic compounds. 5
ACCEPTED MANUSCRIPT However, Gibbs energies of GdNi and GdNi2 at 1113K are -78.5 and -66.3 (kJ/mol. at.) respectively while the assessed values are -38.3 and -47.2 (kJ/mol. at.). The disagreement is noticeable. On the other hand, if we considered both the enthalpies of formation measured by calorimetry and the Gibbs energies of formation determined by Nourry et al. [40] for the GdNi and GdNi2 intermetallic compounds, the relative entropies of formation must become largely negative, which is not reasonable from thermodynamic viewpoint. Thus, we the think that the Gibbs energy of formation of GdNi and GdNi2 determined by Nourry et al. [40] are not reliable.
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Conclusion
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The experimental phase equilibria and the thermodynamic data relative to the Gd–Ni system available in the literature have been critically evaluated. Within the scheme of the CALPHAD technique, the thermodynamic models for all the solution phases and intermediate compounds were selected and the Gibbs energy functions were optimized. A set of consistent thermodynamic parameters was obtained for the Gd–Ni system. The calculated phase equilibria agree well with the recent experimental one established by Xu et al. [32]. The thermodynamic data, such enthalpies of mixing of liquid, standard enthalpies and Gibbs free energies of formation of the Gd–Ni intermetallic compounds, were confronted to the available values from the literature.
Appendix
The Gibbs free energies of the pure elements (solid and liquid) in the stable and metastable states, taken from SGTE database [16]. The data are given in J/mol of atoms.
(298.15
GLIQNi = +16414.686 - 9.397T + GHSERNi − 3.82318.10-21T7 = − 9549.775 + 268.598T − 43.1TLn (T)
(298.15
Gadolinium
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Nickel GHSERNi = − 5179.159 + 117.854T − 22.096TLn (T) − 0.0048407T2 = − 27840.655+279.135T − 43.1TLn (T) + 1.12754.1031T-9
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GHSERGd = − 6834.5855 + 97.13101T − 24.7214131TLn (T) − 0.00285240521T2 (200.00
(200.00
(200.00 < T< 1000.00)
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= + 152792.743 − 1349.58873T + 180.097094TLn (T) − 0.119550229T2 + 1.17915728.10-5T3 − 22038836T-1 = − 15783.7618 + 202.222057T − 38.960425TLn (T) = − 19850.5562 + 224.817909T − 41.904333TLn (T) + 8.58222759.10-4T2 − 3.77570269.10-8T3 + 995428.573T-1
(1000.00
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[33] I. V. Nikolaenko, Ivz. Akad. Nauk. SSSR Met. 4 (1990) 191. [34] C. Colinet, A. Pasturel, K.H. I. Buschow, Met. Trans. Z7A (1986) 777. [35] J. Schott, F. Sommer, J. Less-Common Met. 119 (1986) 307. [36] S. Deodhar, P.J Ficalora, Met. Trans. 6A, (1975) 1909. [37] Q. Guo, O.J. Kleppa, J. Alloys Comp. 270 (1998) 212. [38] Q. Guo, O. J. Kleppa, J. Alloys Comp. 221 (1995) 45. [39] A.R. Miedema, P.F. de Chatel, F.R. de Boer, physica B 100 B (1980) 1. [40] C. Nourry, L. Massot, P. Chamelot, P. Taxil, J. Appl. Electrochem. 39 (2009) 927. [41] G. Bruzzone, M.L. Fomasini, F. Merlo, J. Less-Common Met. 25 (1971) 295. [42] R. Lemaire, D. Paccard, Bull. Soc. Fr. Mineral. Cristallogr. 90 (1967) 311. [43] A. Raman, Inorg. Chem. 7 (1968) 973. [44] M.I. Slanicka, K.N.R.Taylor, G.J. Primavesi, J. Phys. F 1 (1971) 679. [45] A.V. Virkar, A. Raman, J. Less-Common Met. 18 (1969) 59. [46] N.C. Baenziger, J.L. Moriarty, Acta Cryst. 14 (1961) 948. [47] K.H.J. Buschow, J. Less-Common Met. 11 (1966) 204. [48] T.B. Massalski et al. (Eds.), Binary Alloy Phase Diagrams, 1–3, 2nd Edition, Metals Park, OH, USA, 1990. [49] B. Jansson, Ph.D. Thesis, Royal Institute of Technology, Stockholm, Sweden, 1984. [50] H. Okamoto, T.B. Massalski, J. Phase Equilib. 14 (3) (1993) 316. [51] H. Okamoto, T.B. Massalski, J. Phase Equilib. 15 (5) (1994) 500. [52] K.A. Gschneidner, Jr., B.J. Beaudry, Scripta Metall. Mater.25 (1991) 745; and K.A. Gschneidner, Jr., J. Alloys Comp. 193 (1993) 1. [53] Y.U. Kwon, M.A. Rzeznik, A. Guloy, J.D. Corbett, Chem. Mater. 2 (1990) 546. [54] E.A. Leon-Escamilla, J.D. Corbett, J. Alloys Comp. 206 (1994) 115.
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ACCEPTED MANUSCRIPT Figure captions
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Fig. 1. The Gd–Ni phase diagram calculated in this work. Fig. 2. Calculated Gd–Ni phase diagram compared with available experimental data. Fig. 3. Calculated enthalpies of formation of the Gd–Ni intermetallic compounds with available literature data. Fig. 4. Calculated enthalpy of mixing of the liquid phase at 1750 K. Experimental data are the calorimetric results from [33]. Fig. 5. Gibbs energies of formation of Gd–Ni intermetallic compounds at 1113 K.
Table captions
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Table 1. Curie temperatures of some intermediate phases in the Gd–Ni system. Table 2. Gd–Ni Crystal structures data. Table 3. Thermodynamic parameters of the Gd–Ni binary system. Table 4. Calculated and experimental invariant equilibria in the Gd–Ni system.
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ACCEPTED MANUSCRIPT Intermetallic compound [Ref.]
31
[18]
GdNi 69
[19]
GdNi2 80
[20]
GdNi3 114
[21]
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Curie temperature (K)
GdNi5
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α-Gd c β-Gd Gd3Ni Gd3Ni GdNi GdNi2 GdNi3 Gd2Ni7
hP2 cI2 oP16 oC8 cF24 hR24 hP36 hR54
GdNi5 Gd2Ni17 Ni
hP6 hP38 cF4
Mg W Fe3C CrB Cu2Mg PuNi3 a Ce2Ni7 b Gd2Co7 CaCu5 Th2Ni17 Cu
d
Symbol used in Thermo-Calc data file HCP_A3 BCC_A2 Gd3Ni_LT Gd3Ni_HT GdNi GdNi2 GdNi3 Gd2Ni7
Reference
[41] [41] [42] [32] [43] [44] [45] [25]
GdNi5 Gd2Ni17 FCC_A1
[46] [47] [48]
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Pearson symbol
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Phase
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a: high-temperature form. b: low-temperature form. c: from 1508 K to 1586 K. d: below 1508 K.
ACCEPTED MANUSCRIPT Phase Liquid
Thermodynamic parameters
a
LGd ,Ni = −155033.136 + 61.479 ×T
0
LGd ,Ni = 85320.912 − 36.759 ×T
1
LGd ,Ni = 104
FCC_A1
0
HCP_A3
0
BCC_A2
0
Gd3Ni_LT
hcp G Gd 3 Ni _ LT = 0.75 0G Gd + 0.250 G Nifcc − 16661 + 3.730 ×T
Gd3Ni_HT
hcp G Gd 3 Ni _ HT = 0.75 0G Gd + 0.250 G Nifcc − 16304 + 3.338 ×T
GdNi
hcp GGdNi = 0.500GGd + 0.50 0G Nifcc − 31426 + 6.721×T
GdNi2
hcp GGdNi 2 = 0.330GGd + 0.67 0G Nifcc − 36015 + 9.772 ×T
GdNi3
hcp GGdNi 3 = 0.250GGd + 0.75 0G Nifcc − 35127 + 10.012 ×T
Gd2Ni7
hcp GGd 2 Ni 7 = 0.22 0GGd + 0.780G Nifcc − 34819 + 10.345 ×T
GdNi5
hcp GGdNi 5 = 0.170GGd + 0.83 0G Nifcc − 29767 + 8.271×T
Gd2Ni17
hcp GGd 2Ni17 = 0.110GGd + 0.89 0G Nifcc − 21404 + 7.063 ×T
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Gibbs energies are expressed in (J/mol.at.)
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LGd ,Ni = 104
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a
LGd ,Ni = 104
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Temperature (K) This work 1039
911
1039 986 1008 1006 911
[32] [29] [26] [28] [32]
Gd3Ni_LT ↔ Gd3Ni_HT
Allotropic transition Eutectic
977
977
[32]
Congruent
1238
Liquid ↔ GdNi + GdNi2
Eutectic
1172
Liquid + GdNi3 ↔ GdNi2
Peritectic
Liquid + Gd2Ni7 ↔ GdNi3
Peritectic
1238 1253 1553 1172 1158 1153 1232 1358 1268 1283 1280 1480 1383 1383 1372 1557 1473 1473 1474 1706 1753 1760 1589 1573 1558 1553 1571 1563 1548 1521
[32] [29] [26] [32] [29] [26] [28] [32] [29] [26] [28] [32] [29] [26] [28] [32] [29] [26] [28] [29] [26] [28] [32] [29] [26] [28] [32] [29] [26] [28]
Liquid ↔ Gd3Ni_HT + GdNi
Peritectic
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Liquid + GdNi5 ↔ Gd2Ni7
1358
1481
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Liquid ↔ GdNi
1556
Congruent
1705
Liquid + GdNi5 ↔ Gd2Ni17
Peritectic
1589
Liquid ↔ Gd2Ni17 + Ni
Eutectic
1571
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Liquid ↔ GdNi5
32
30 28
-
36
[32] [28]
-
33
-
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Peritectic
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Liquid + α-Gd ↔ Gd3Ni_HT
Literature data [Ref.]
Composition of the liquid phase (at. % Ni) This work Literature data [Ref.]
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Reaction
[32] -
56
56 56 57
[32] [26] [28]
64
61 58 57
[32] [26] [28]
69
66 61 60
[32] [26] [28]
73
71 65 64
[32] [26] [28]
-
-
91
90 94 95
[32] [26] [28]
93
94 95 96
[32] [26] [28]
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S0925-8388(15)30320-0
DOI:
10.1016/j.jallcom.2015.06.201
Reference:
JALCOM 34608
To appear in:
Journal of Alloys and Compounds
Received Date: 18 May 2015 Revised Date:
23 June 2015
Accepted Date: 24 June 2015
Please cite this article as: Z. Rahou, K. Mahdouk, Thermodynamic reassessment of Gd–Ni system, Journal of Alloys and Compounds (2015), doi: 10.1016/j.jallcom.2015.06.201. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Thermodynamic reassessment of Gd–Ni system Z. Rahou∗ and K. Mahdouk Laboratory of Thermodynamics and Energetics (L.T.E), Faculty of Sciences, Ibn Zohr University, B.P. 8106, Agadir, Morocco. ∗ Corresponding author; phone: +212-661625347; email: [email protected].
Abstract
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By means of CALPHAD (CALculation of PHAse Diagrams) approach, the phase diagram and thermodynamic data of the Gd–Ni system were critically assessed. The Gd–Ni system contains four solution phases (liquid, face-centered cubic FCC_A1, body-centered cubic BCC_A2 and hexagonal close-packed HCP_A3) modeled with the Redlich-Kister polynomials and seven intermetallic compounds Gd3Ni, GdNi, GdNi2, GdNi3, Gd2Ni7, GdNi5 and Gd2Ni17, which are all treated as stoichiometric compounds. A set of self-consistent thermodynamic parameters describing various phases in this binary system was obtained. The phase diagram and thermodynamic quantities calculated from assessed parameters agree well with experimental data.
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Keywords: Gd–Ni system, thermodynamic assessment, phase diagram, Calphad approach.
1. Introduction
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The intermetallic compounds formed by rare earth (RE) elements and transition metals (TM) are of particular interest regarding to their potential usage as high value functional materials, such as permanent magnets [1,2] and hydrogen storage materials (reversible absorption of a large quantity of hydrogen gas at room temperature and nearly at atmospheric pressure) [3,4]. Moreover, many ternary Al–TM–RE systems form amorphous alloys with interesting mechanical properties [5] and some rare-earth/transition metal oxides are candidate materials for solid oxide fuel cells [6]. Furthermore, the rare-earth/3d transition metal intermetallic compounds were suggested as being promising candidates for room temperature magnetic refrigeration based on magneto-caloric effect (MCE) [7,8] who has attracted more attention for improved energy efficiency and environmental friendliness compared with traditional compression/expansion gas refrigeration [9,10].
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On the other hand, the knowledge of thermodynamic data and phase diagrams is essential for developing and checking models of phase transformations, coupling thermodynamics with kinetics [11]. The purpose of the present work is (1) to evaluate recent experimental phase diagram and his relative thermodynamic data and (2) to provide a set of self-consistent parameters for calculation of the phase equilibria and thermodynamic properties in the Gd–Ni binary system using the CALPHAD method [12] and the Thermo-Calc software package [13].
2. Thermodynamic models 2.1. Pure elements The stable forms of the pure elements at 298.15K and 1 bar were chosen as the reference states of the system. For the thermodynamic functions of the pure elements in their stable and metastable states, the phase stability for the element i in ϕ status is given as: 0 φ ( T ) = G φ ( T ) − H SER = a + bT + cT ln T + dT 2 + eT 3 + fT − 1 + gT 7 + hT − 9 Gi i i
1
(1)
ACCEPTED MANUSCRIPT where H iSER (298.15 K ) is the molar enthalpy of the so-called “Standard Element Reference” (SER), i.e., the enthalpies of the pure elements in their defined reference state at 298.15 K and 1 bar; T is the absolute temperature; Giφ (T ) is the absolute molar Gibbs energy of the element i (i = Gd and Ni) with structure ϕ in a non magnetic states. In thermodynamic study, absolute energy is not of importance, so the relative value of Gibbs energy 0Giφ (T ) is adopted in CALPHAD approach. The Gibbs energy of the element i, 0Giφ (T ) , in its
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SER state is denoted by GHSERi , i.e. hcp 0 hcp SER GHSERGd = GGd (T ) = GGd (T ) − H Gd (298.15K ) fcc 0 fcc SER GHSERNi = GNi (T ) = GNi (T ) − H Ni (298.15 K )
(2)
(3)
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In the present work, the Gibb energy for the pure element Ni was taken from the SGTE compilation of Dinsdale [14], while that relative to the pure element Gd was taken from the work of Huasen et al. [15] who has evaluated the properties of the Gd element. We note that Dinsdale [16] has recently updated his SGTE-Pure database to incorporate the work of Huasen et al. [15].
2.2. Solution phases
The substitutional solution model was employed to describe the solution phases including Liquid, FCC_A1, BCC_A2 and HCP_A3. The molar Gibbs energy of the solution phase ϕ (ϕ = Liquid, FCC_A1, HCP_A3 and BCC_A2) can be expressed as: mg φ φ 0 φ 0 φ E φ Gm +
Gm
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G m = x Gd GGd + x Ni G Ni + RT ( x Gd Lnx Gd + x Ni Lnx Ni ) +
(4)
where Gmφ is the molar Gibbs energy of a solution phase ϕ; 0Giφ is the molar Gibbs energy of the element i (i = Gd or Ni) with the structure ϕ in a non-magnetic state; xi the mole fraction of component i, R gas constant, T temperature; EGmφ the excess Gibbs energy, and
mg
G mφ is the magnetic
φ
G m = x Gd x Ni ∑ j
j φ j LGd , Ni ( x Gd − x Ni )
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contribution to the Gibbs energy. The excess Gibbs energy of phase ϕ can be expressed by the Redlich–Kister polynomials [17] as: (5)
j φ here LGd , Ni (j = 0, 1, 2,…) is the interaction parameter between elements Gd and Ni and is
formulated as temperature dependent : j φ
LG d , N i = a j + b j T + c j TLnT + d j T
2
+ e jT
3
+ f jT
−1
+ g jT
7
+ hjT
−9
(6)
where aj, bj, cj, dj, ej, fj, gj and hj are model parameters to be optimized. In most cases, only the two first terms of the above equation are used.
2.3. Intermetallic compounds All the intermetallic compounds α-Gd3Ni, β-Gd3Ni, GdNi, GdNi2, GdNi3, Gd2Ni7, GdNi5 and Gd2Ni17 were treated as stoichiometric phases in the Gd–Ni binary system because no available experimental data reports the existence of an homogeneity range for these compounds. The Gibbs 2
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Gd Ni Gm A B =
A
0
A + B
hcp GGd +
B A + B
0
fc c m g G d A N iB G N i + a + bT + Gm
(7)
hcp where 0 GGd and 0 G Nfci c are the Gibbs energies of the respective pure elements Gd and Ni in the non-
magnetic hcp and fcc structure respectively. The parameters a and b are evaluated in the present work.
GmGd A NiB is the magnetic contribution to the Gibbs energy.
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mg
As can be seen in table 1, the Curie temperatures of the intermetallic compounds in the Gd–Ni system, available in the literature, are much below 298.15 K. For this reason, we have not taken into account the contribution of the magnetic term in our calculations.
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3. Bibliographic description of the Gd–Ni system 3.1 Equilibrium diagram
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The Gd–Ni phase diagram has been investigated in 1961 by Spedding et al. [22], Novy et al. [23] and Copeland and Kato [24]. The three diagrams are in a general agreement, showing two congruent melting compounds and three eutectic reactions. Note that Gd2Ni17 with a stoichiometric ratio of 2:17 reported by Novy et al. [23] was widely accepted although a ratio of 2:15 proposed by Copeland et al. [24].
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Buschow and Van Der Goot [25] examined annealed samples of Gd2Ni7 for 2 to 4 weeks. They found that the main phase was hexagonal when samples were quenched from 1200 °C and rhombohedral when annealed at 700 °C. Consequently, they suggested that the hexagonal structure is the high-temperature form, and the rhombohedral type is the low-temperature form. Both of these structures always coexisted in the studied samples, and the temperature of the allotropic transition was not determined.
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The Gd–Ni phase diagram was experimentally reinvestigated in 1986 by Pan et al. [26] using X-ray diffraction (XRD) and differential thermal analysis (DTA) and assessed in 1991 by Pan and Nash [27]. The following nine phases were supposed to exist: Gd3Ni, Gd3Ni2, GdNi, GdNi2, GdNi3, Gd2Ni7, GdNi4, GdNi5 and Gd2Ni17. Among these compounds, GdNi and GdNi5 melt congruently, while the others are formed by peritectic reactions. Three eutectic reactions occur: L↔ Gd3Ni + Gd3Ni2 (635℃, ～32 at.% Ni), L ↔ GdNi2 + GdNi2 (880℃～56 at.% Ni) and L ↔ Gd2Ni17 + fcc-Ni (1275℃, ～95 at.% Ni). Neither Gd in Ni nor Ni in Gd exhibits any detectable solid solubility [26]. The experimental results obtained by Pan et al. [26] and by Copeland and Kato [24] have been used for a thermodynamic assessment carried out by Xia and Jin [28] using the CALPHAD technique. However, the results obtained by these authors present large discrepancies with the experimental data, and the calculated enthalpies of formation are too less negative and seem to be inconsistent. Using XRD at room temperature, DTA, electromotive force (EMF) measurements, Dischinger and Schaller [29] investigated this phase diagram over the entire range of composition. In comparison with the data of Pan et al. [26] there is an excellent accordance concerning the peritectic and the eutectic temperatures and a good accordance concerning the melting point of the compound GdNi5. However, a discrepancy of about 300 K exists concerning the melting point of the GdNi compound.
3
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More recently, the Gd–Ni phase equilibria was critically reinvestigated by Xu et al. [32] using scanning electron microscopy with energy-dispersive X-ray spectrometry (SEM/EDS), XRD and differential scanning calorimeter (DSC) measurements realized on samples over the entire composition range. Except the confirmation of the absence of Gd3Ni2 and GdNi4 compounds, the shape of this recent phase diagram is consistent with the results of Dischinger and Schaller [29]. However, discrepancies with the results of Pan et al. [26] was noted especially regarding the congruent melting temperature of GdNi. In the work by Xu et al. [32], the DSC curve for the Gd-20 at.% Ni sample exhibits a small pic at 911 K attributed by these authors to an allotropic transformation of Gd3Ni.
3.2 Thermodynamic data
3.3 Crystallographic data
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Many researchers investigated the thermodynamic properties of Gd–Ni intermetallic compounds. The enthalpies of mixing of liquid alloys were determined at 1750 K over the entire range of composition by Nikolaenko [33]. Enthalpies of formation for several Gd–Ni intermetallic compounds have been determined by calorimetry by Colinet et al. [34], Schott and Sommer [35] and Deodhar and Ficalora [36]. Using direct synthesis calorimetry, Guo and Kleppa [37,38] measured the standard enthalpies of formation of GdNi and GdNi5 compounds. Nourry et al. [40] measured experimentally the Gibbs energies of formation of some Gd–Ni intermetallic compounds. The predicted enthalpies of formation of Gd–Ni alloys from the semi-empirical model of Miedema et al. [39] are also available in the literature.
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The available crystallographic data of Gd–Ni intermediate phases are compiled in Table 2.
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4. Assessment procedure
The thermodynamic optimization of the model parameters of the Gibbs energy expressions is an application of the CALPHAD technique with the help of the PARROT module of the Thermo-Calc software developed by Jansson [49] and Sundman et al. [13]. Its procedure consists of the choice of thermodynamic models for the Gibbs energy of the individual phases as previously described, the analysis of the all related experimental data available, and the computer-aided nonlinear for minimizing the square sum of the errors between the experimental data and the computed values. In the beginning of the assessment, each set of experimental data was given a certain weight. The weights were changed systematically during the optimization until most of experimental data was accounted for within the claimed uncertainty limits. The optimization was carried out by steps. The thermodynamic parameters for the intermetallic compounds were optimized at the first stage based on the available experimental standard enthalpies of formation for the Gd–Ni intermetallic compounds and the phase boundaries information. Then experimental data related to invariant equilibria have been added to the calculation. All the parameters were finally evaluated together to give the best 4
ACCEPTED MANUSCRIPT description of the system. We note that we have neglected the solubilities in the FCC_ A1, BCC_A2 and HCP_A3 terminal solid solutions in accord with the recent experimental results [32]. This was realized by assigning a large positive value to the j LφNi ,Gd interaction parameter of Eq (5), i.e. 0
L GH dC P, N _i A 3 =
0
L GB Cd C, N _i A 2 =
0
L GF Cd C, N_i A 1 = 1 0 4
(7)
5. Results and discussion
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Thermodynamic parameters for all condensed phases in the Gd–Ni binary system obtained in the present work are summarized in Table 3. In Table 4, we give invariant reactions data for this binary system. Good agreement has been realized between the calculated results and the recent experimental data reported by Xu et al. [32].
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The calculated phase diagram of the Gd–Ni system is illustrated in Fig. 1. In Fig. 2 we compare our calculated phase diagram with the experimental data reported by Xu et al. [32], Pan et al. [26] and Dischinger and Schaller [29]. The phase diagram obtained in this work is in good agreement with that established recently by Xu et al. [32]. The incompatible asymmetry of the liquidus phase [50,51] on the left and right sides of the GdNi5 compound was corrected in the course of this study (Fig.2). Indeed, according to Okamoto and Massalski’s studies [50, 51], judgment about asymmetry of liquidus curves can be made comparing the ratio of the width of the two phase fields on each side of a compound at the same temperature. If the width on one side of the compound is either one half or double that on the other side, the asymmetry may be considered clearly unusual.
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As mentioned previously, the enthalpies of formation of the Gd–Ni intermetallic compounds are measured by several authors. In general, direct calorimetric measurements are considered to be the most reliable, so the values obtained by Guo and Kleppa [37, 38] were used in the present study with high weights. Fig. 3 shows the standard enthalpies of formation of Gd–Ni intermediate phases together with the predicted values by the Miedema model [39] and with the experimental data determined by Colinet et al. [34], Schott and Sommer [35], Deodhar and Ficalora [36] and Guo and Kleppa [37, 38]. A reasonable agreement is noted between the calculated results and the experimental values determined by calorimetry. The enthalpies of formation for many compounds predicted by Miedema model [39] are usually more exothermic compared to the calorimetric data and they may be considered using precaution. The enthalpy of formation determined by Deodhar and Ficalora [36] for GdNi2 using calorimetry [36] is less negative than our calculated one. This value is also less negative compared to the other experimental values obtained by Colinet et al. [34] and Schott and Sommer [35]. The discrepancy between the experimental results is certainly due to the relative purity of the starting materials [52,53] and to the fact that the rare earth elements are largely reactive with crucibles and containers, particularly at high temperatures [54]. We note that the enthalpies of formation of Gd3Ni and GdNi2 calculated by Xia and Jin [28] are too less negatives and differ from the experimental values of Colinet et al. [34] by 13.5 kJ/mol and 23.7 kJ/mol respectively. Fig. 4 presents the calculated enthalpy of mixing of liquid at 1750K in the Gd–Ni system with the experimental data determined by Nicolaenko [33]. The calculated values are satisfactorily consistent with the measured data in Ref. [33]. Gibbs energies of formation of intermetallic compounds at 1113K were further calculated and compared with data measured by Nourry et al. [40] in Fig. 5. Good agreement was realized between the calculated values and experimental results for GdNi5 and GdNi3 intermetallic compounds. 5
ACCEPTED MANUSCRIPT However, Gibbs energies of GdNi and GdNi2 at 1113K are -78.5 and -66.3 (kJ/mol. at.) respectively while the assessed values are -38.3 and -47.2 (kJ/mol. at.). The disagreement is noticeable. On the other hand, if we considered both the enthalpies of formation measured by calorimetry and the Gibbs energies of formation determined by Nourry et al. [40] for the GdNi and GdNi2 intermetallic compounds, the relative entropies of formation must become largely negative, which is not reasonable from thermodynamic viewpoint. Thus, we the think that the Gibbs energy of formation of GdNi and GdNi2 determined by Nourry et al. [40] are not reliable.
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Conclusion
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The experimental phase equilibria and the thermodynamic data relative to the Gd–Ni system available in the literature have been critically evaluated. Within the scheme of the CALPHAD technique, the thermodynamic models for all the solution phases and intermediate compounds were selected and the Gibbs energy functions were optimized. A set of consistent thermodynamic parameters was obtained for the Gd–Ni system. The calculated phase equilibria agree well with the recent experimental one established by Xu et al. [32]. The thermodynamic data, such enthalpies of mixing of liquid, standard enthalpies and Gibbs free energies of formation of the Gd–Ni intermetallic compounds, were confronted to the available values from the literature.
Appendix
The Gibbs free energies of the pure elements (solid and liquid) in the stable and metastable states, taken from SGTE database [16]. The data are given in J/mol of atoms.
(298.15
GLIQNi = +16414.686 - 9.397T + GHSERNi − 3.82318.10-21T7 = − 9549.775 + 268.598T − 43.1TLn (T)
(298.15
Gadolinium
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Nickel GHSERNi = − 5179.159 + 117.854T − 22.096TLn (T) − 0.0048407T2 = − 27840.655+279.135T − 43.1TLn (T) + 1.12754.1031T-9
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GHSERGd = − 6834.5855 + 97.13101T − 24.7214131TLn (T) − 0.00285240521T2 (200.00
(200.00
(200.00 < T< 1000.00)
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= + 152792.743 − 1349.58873T + 180.097094TLn (T) − 0.119550229T2 + 1.17915728.10-5T3 − 22038836T-1 = − 15783.7618 + 202.222057T − 38.960425TLn (T) = − 19850.5562 + 224.817909T − 41.904333TLn (T) + 8.58222759.10-4T2 − 3.77570269.10-8T3 + 995428.573T-1
(1000.00
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[33] I. V. Nikolaenko, Ivz. Akad. Nauk. SSSR Met. 4 (1990) 191. [34] C. Colinet, A. Pasturel, K.H. I. Buschow, Met. Trans. Z7A (1986) 777. [35] J. Schott, F. Sommer, J. Less-Common Met. 119 (1986) 307. [36] S. Deodhar, P.J Ficalora, Met. Trans. 6A, (1975) 1909. [37] Q. Guo, O.J. Kleppa, J. Alloys Comp. 270 (1998) 212. [38] Q. Guo, O. J. Kleppa, J. Alloys Comp. 221 (1995) 45. [39] A.R. Miedema, P.F. de Chatel, F.R. de Boer, physica B 100 B (1980) 1. [40] C. Nourry, L. Massot, P. Chamelot, P. Taxil, J. Appl. Electrochem. 39 (2009) 927. [41] G. Bruzzone, M.L. Fomasini, F. Merlo, J. Less-Common Met. 25 (1971) 295. [42] R. Lemaire, D. Paccard, Bull. Soc. Fr. Mineral. Cristallogr. 90 (1967) 311. [43] A. Raman, Inorg. Chem. 7 (1968) 973. [44] M.I. Slanicka, K.N.R.Taylor, G.J. Primavesi, J. Phys. F 1 (1971) 679. [45] A.V. Virkar, A. Raman, J. Less-Common Met. 18 (1969) 59. [46] N.C. Baenziger, J.L. Moriarty, Acta Cryst. 14 (1961) 948. [47] K.H.J. Buschow, J. Less-Common Met. 11 (1966) 204. [48] T.B. Massalski et al. (Eds.), Binary Alloy Phase Diagrams, 1–3, 2nd Edition, Metals Park, OH, USA, 1990. [49] B. Jansson, Ph.D. Thesis, Royal Institute of Technology, Stockholm, Sweden, 1984. [50] H. Okamoto, T.B. Massalski, J. Phase Equilib. 14 (3) (1993) 316. [51] H. Okamoto, T.B. Massalski, J. Phase Equilib. 15 (5) (1994) 500. [52] K.A. Gschneidner, Jr., B.J. Beaudry, Scripta Metall. Mater.25 (1991) 745; and K.A. Gschneidner, Jr., J. Alloys Comp. 193 (1993) 1. [53] Y.U. Kwon, M.A. Rzeznik, A. Guloy, J.D. Corbett, Chem. Mater. 2 (1990) 546. [54] E.A. Leon-Escamilla, J.D. Corbett, J. Alloys Comp. 206 (1994) 115.
8
ACCEPTED MANUSCRIPT Figure captions
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Fig. 1. The Gd–Ni phase diagram calculated in this work. Fig. 2. Calculated Gd–Ni phase diagram compared with available experimental data. Fig. 3. Calculated enthalpies of formation of the Gd–Ni intermetallic compounds with available literature data. Fig. 4. Calculated enthalpy of mixing of the liquid phase at 1750 K. Experimental data are the calorimetric results from [33]. Fig. 5. Gibbs energies of formation of Gd–Ni intermetallic compounds at 1113 K.
Table captions
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Table 1. Curie temperatures of some intermediate phases in the Gd–Ni system. Table 2. Gd–Ni Crystal structures data. Table 3. Thermodynamic parameters of the Gd–Ni binary system. Table 4. Calculated and experimental invariant equilibria in the Gd–Ni system.
9
ACCEPTED MANUSCRIPT Intermetallic compound [Ref.]
31
[18]
GdNi 69
[19]
GdNi2 80
[20]
GdNi3 114
[21]
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Curie temperature (K)
GdNi5
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α-Gd c β-Gd Gd3Ni Gd3Ni GdNi GdNi2 GdNi3 Gd2Ni7
hP2 cI2 oP16 oC8 cF24 hR24 hP36 hR54
GdNi5 Gd2Ni17 Ni
hP6 hP38 cF4
Mg W Fe3C CrB Cu2Mg PuNi3 a Ce2Ni7 b Gd2Co7 CaCu5 Th2Ni17 Cu
d
Symbol used in Thermo-Calc data file HCP_A3 BCC_A2 Gd3Ni_LT Gd3Ni_HT GdNi GdNi2 GdNi3 Gd2Ni7
Reference
[41] [41] [42] [32] [43] [44] [45] [25]
GdNi5 Gd2Ni17 FCC_A1
[46] [47] [48]
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Pearson symbol
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Phase
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a: high-temperature form. b: low-temperature form. c: from 1508 K to 1586 K. d: below 1508 K.
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Thermodynamic parameters
a
LGd ,Ni = −155033.136 + 61.479 ×T
0
LGd ,Ni = 85320.912 − 36.759 ×T
1
LGd ,Ni = 104
FCC_A1
0
HCP_A3
0
BCC_A2
0
Gd3Ni_LT
hcp G Gd 3 Ni _ LT = 0.75 0G Gd + 0.250 G Nifcc − 16661 + 3.730 ×T
Gd3Ni_HT
hcp G Gd 3 Ni _ HT = 0.75 0G Gd + 0.250 G Nifcc − 16304 + 3.338 ×T
GdNi
hcp GGdNi = 0.500GGd + 0.50 0G Nifcc − 31426 + 6.721×T
GdNi2
hcp GGdNi 2 = 0.330GGd + 0.67 0G Nifcc − 36015 + 9.772 ×T
GdNi3
hcp GGdNi 3 = 0.250GGd + 0.75 0G Nifcc − 35127 + 10.012 ×T
Gd2Ni7
hcp GGd 2 Ni 7 = 0.22 0GGd + 0.780G Nifcc − 34819 + 10.345 ×T
GdNi5
hcp GGdNi 5 = 0.170GGd + 0.83 0G Nifcc − 29767 + 8.271×T
Gd2Ni17
hcp GGd 2Ni17 = 0.110GGd + 0.89 0G Nifcc − 21404 + 7.063 ×T
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Gibbs energies are expressed in (J/mol.at.)
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LGd ,Ni = 104
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a
LGd ,Ni = 104
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Temperature (K) This work 1039
911
1039 986 1008 1006 911
[32] [29] [26] [28] [32]
Gd3Ni_LT ↔ Gd3Ni_HT
Allotropic transition Eutectic
977
977
[32]
Congruent
1238
Liquid ↔ GdNi + GdNi2
Eutectic
1172
Liquid + GdNi3 ↔ GdNi2
Peritectic
Liquid + Gd2Ni7 ↔ GdNi3
Peritectic
1238 1253 1553 1172 1158 1153 1232 1358 1268 1283 1280 1480 1383 1383 1372 1557 1473 1473 1474 1706 1753 1760 1589 1573 1558 1553 1571 1563 1548 1521
[32] [29] [26] [32] [29] [26] [28] [32] [29] [26] [28] [32] [29] [26] [28] [32] [29] [26] [28] [29] [26] [28] [32] [29] [26] [28] [32] [29] [26] [28]
Liquid ↔ Gd3Ni_HT + GdNi
Peritectic
EP
Liquid + GdNi5 ↔ Gd2Ni7
1358
1481
TE D
Liquid ↔ GdNi
1556
Congruent
1705
Liquid + GdNi5 ↔ Gd2Ni17
Peritectic
1589
Liquid ↔ Gd2Ni17 + Ni
Eutectic
1571
AC C
Liquid ↔ GdNi5
32
30 28
-
36
[32] [28]
-
33
-
SC
Peritectic
M AN U
Liquid + α-Gd ↔ Gd3Ni_HT
Literature data [Ref.]
Composition of the liquid phase (at. % Ni) This work Literature data [Ref.]
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Reaction
[32] -
56
56 56 57
[32] [26] [28]
64
61 58 57
[32] [26] [28]
69
66 61 60
[32] [26] [28]
73
71 65 64
[32] [26] [28]
-
-
91
90 94 95
[32] [26] [28]
93
94 95 96
[32] [26] [28]
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